Answer:
Hence, the distance of the ship from initial position is:
498.977 miles.
Step-by-step explanation:
We will apply the cosine law to calculate the distance of the cruise ship from the initial position.
The cosine law is given as:
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
where a is the distance covered by the ship in east direction.
b is the distance covered by ship in the north-east direction.
and c is the distance of the ship from the initial point.
The angle C is the angle between a and b and is given by:
C=155°.
Here we have: a=330 miles, b=180 miles.
Hence, we apply the cosine law to obtain:
[tex]c^2=(330)^2+(180)^2-2\times 330\times 180\times \cos 155\\\\c^2=108900+32400-118800\times (-0.906308)\\\\c^2=248977.944\\\\c=498.977[/tex]
Hence, the distance of the ship from initial position is:
498.977 miles.
